Three blocks of masses 2 kg , 3 kg and 5 kg are connected to each other with light string and are then placed on a smooth frictionless surface. The system is pulled with force F from side of the lighter mass so that it moves with an acceleration of 1 ms -2, T 1 and T 2 denote the tension in the other strings. The value of F is

Question

Three blocks of masses 2 kg , 3 kg and 5 kg are connected to each other with light string and are then placed on a smooth frictionless surface. The system is pulled with force F from side of the lighter mass so that it moves with an acceleration of 1 ms -2, T 1 and T 2 denote the tension in the other strings. The value of F is (A) 30 N (B) 20 N (C) 10 N (D) 40 N

Tardigrade Admin · Accepted Answer

Equations of motions are for 2 kg. block, F - T 1=2 a ldots (i) for 3 kg block, T 1- T 2=3 a ldots (ii) For 5 kg block T 2=5 a(iii) putting the value of T 2 in eq (ii) ∴ T 1-5 a =3 a ⇒ T 1=8 a [Putting in eq (i)] F-8 a=2 a ⇒ F=10 N ( a =1 m / s 2)

$30 N$

$20 N$

$10 N$

$40 N$

30N

20N

10N

40N

Equations of motions are for 2kg. block, F−T1​=2a…(i) for 3kg block, T1​−T2​=3a… (ii) For 5kg block T2​=5a(iii) putting the value of T2​ in eq (ii) ∴T1​−5a=3a⇒T1​=8a [Putting in eq (i)] F−8a=2a⇒ F=10N(a=1m/s2)

$30 N$

$20 N$

$10 N$

$40 N$